Theresa May is set to announce major government action to improve support for people struggling with mental illness, including moves to help troubled young people and reduce the number of suicides.

In a rare speech on domestic policy on Monday, the prime minister will promise that the whole of government will do more to improve the care received by the one in four people every year who develop anxiety, depression or other related conditions.

She will detail how employers can play a much bigger role in helping staff who are forced to take time off work as a result of mental health problems. She is also finalising plans to outline steps schools can take to better identify and help the growing number of pupils who are becoming mentally vulnerable, sometimes as a result of sexting, bullying and pressure to do well in exams.

May’s move will be the climax of a concerted attempt by the prime minister, starting this weekend, to show that she is determined to make progress on the social justice agenda that she described on her first day in Downing Street as the “burning injustices” in society. “If you suffer from mental health problems, there’s not enough help to hand,” she said.

The prime minister has been interested in mental illness and its consequences since learning during her six years as home secretary how much police time is taken up dealing with the issue and the very high number of prisoners who have serious psychological or psychiatric conditions.

Mental health charities have praised May’s record on the subject, which included a big drop in the number of people in acute distress who were put in a police cell to undergo an assessment of their mental state because there was no other available “place of safety” nearby.

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The speech will be her first on health, an area in which opponents have criticised her over her claim to be giving the NHS £10bn extra funding by 2020 and a deteriorating record on NHS waiting times for A&E and cancer care and planned operations.

A key element will be an announcement of new measures to reduce the number of people taking their own lives. The number of suicides across the UK fell from 6,232 in 2013 to 6,122 in 2014. Although the rate of of suicide among men is going down, it is rising among women, although 45- to 59-year-olds of both sexes are the likeliest to take their own life.

Opposition MPs urged the PM to use Monday’s speech in central London to unveil meaningful plans to end long waits for mental health treatment and ensure patients did not become so unwell that they ended up in mental health crisis.

“Now is the time for the prime minister to demonstrate that the government’s actions match the rhetoric,” said the Liberal Democrat MP Norman Lamb, who was the mental health minister in the coalition until 2015.

“Now they must end the intolerable discrimination which exists within the NHS. We can no longer tolerate people with mental ill health having to wait interminably for treatment or getting no treatment at all.”

He said May should bring in maximum waiting times for mental health treatment to match those that already exist for physical health, such as A&E treatment, and make mental health a personal priority of her time in power, as her predecessor David Cameron did with dementia.

Luciana Berger, a member of the Commons health select committee and president of the Labour campaign for mental health, said: “The inadequacy of our mental health services is one of the most perilous challenges our NHS and country faces. It can only be solved by tangible change felt in every school, workplace and community.

“It is vital that the prime minister breaks the tradition of broken promises which has so far characterised her party’s approach to mental health. The focus needs to be on early intervention and prevention – services which have been savagely cut since 2010.”

Downing Street officials have been examining how to help schools cope with mental illness. The health secretary, Jeremy Hunt, favours a system, being trialled in 225 schools in 22 parts of England, under which schools can seek advice from an expert working locally in NHS child and adolescent mental healthcare and ensure that pupils are seen more quickly. No 10 has also been looking at overhauling teacher training so that trainees are better able to spot telltale signs of distress and has been advised to ensure mental health is included on the secondary school curriculum to help prepare pupils for confronting what some experts say is an epidemic among under-18s.

May is expected to highlight the damaging role social media can have on young people’s mental welfare. Officials have been exploring potential curbs on the problem. Hunt recently called on mobile phone companies and firms such as Facebook and Twitter to stop under-18s sending sexually explicit images, including setting up parental blocks on their child’s account.

May’s speech will in part be the government’s formal response to the 58 recommendations made last year by NHS England’s mental health taskforce. She will acknowledge that many different departments have a key role to play in improving mental health, including the Department for Work and Pensions (welfare benefits), Ministry of Justice (offenders) and Department for Education (schools), not just the Department of Health and NHS, and promise better performance across Whitehall.

Mental health experts are keen to see if May accepts the taskforce’s plea for the Cabinet Office and Department of Health to create a body to provide “cross-government oversight” of how much progress ministers are making on improving care.

Privately, specialists in the field recalled the creation under Cameron of a cabinet committee to oversee mental health policy, which was disbanded soon afterwards. One leading figure, who asked not to be named, said: “This focus on mental health is welcome and there’s potential for Theresa May to lead on mental health in a way no other prime minister has done. But is there something big she can do to help schools or is that just talk? And can she change the benefits system to help people, or is that just window dressing?”

May will not announce any extra mental health funding beyond the £1bn extra for the sector generally and separate £1.4bn for children and young people’s care, both due to arrive by 2020. One Whitehall source with knowledge of the speech said: “This isn’t about providing new money. It’s about re-evaluating what the priorities in mental health are.”

In the UK, the Samaritans can be contacted on 116 123. In the US, the National Suicide Prevention Hotline is 1-800-273-8255. In Australia, the crisis support service Lifeline is on 13 11 14.